Sheer bliss! Posted by Yermak 3 Feb 2011 05:33 I did it! I figured out this formula! Re: Sheer bliss! give any hint: F[n] = summa(a[i] * F[n-i], i=1..k) are right? (here a[i], and k - are consts). k=? a[]- easy generate, iff k - know. Re: Sheer bliss! Yes, you are right. k = 19. Good luck! :-D Re: Sheer bliss! (n-19>=7) start from 7... Re: Sheer bliss! Hint: solve system equation with Gauss method (19x19).
*Edited by author 31.12.2019 16:33* static constexpr int results[] = { // 0 1 2 3 4 5 0, 0, 0, 0, 0, 0, /*Answer for n = 6 is*/ 12, /*Answer for n = 7 is*/ 46, /*Answer for n = 8 is*/ 144, /*Answer for n = 9 is*/ 110, /*Answer for n = 10 is*/ 312, /*Answer for n = 11 is*/ 290, /*Answer for n = 12 is*/ 670, /*Answer for n = 13 is*/ 706, /*Answer for n = 14 is*/ 1538, /*Answer for n = 15 is*/ 1732, /*Answer for n = 16 is*/ 3504, /*Answer for n = 17 is*/ 4288, /*Answer for n = 18 is*/ 8098, /*Answer for n = 19 is*/ 10568, /*Answer for n = 20 is*/ 19044, /*Answer for n = 21 is*/ 26042, /*Answer for n = 22 is*/ 45222, /*Answer for n = 23 is*/ 64220, /*Answer for n = 24 is*/ 108382, /*Answer for n = 25 is*/ 158324, /*Answer for n = 26 is*/ 261754, /*Answer for n = 27 is*/ 390314, /*Answer for n = 28 is*/ 635666, /*Answer for n = 29 is*/ 962282, /*Answer for n = 30 is*/ 1550244, /*Answer for n = 31 is*/ 2372372, /*Answer for n = 32 is*/ 3792560, /*Answer for n = 33 is*/ 5848746, /*Answer for n = 34 is*/ 9299148, /*Answer for n = 35 is*/ 14419296, /*Answer for n = 36 is*/ 22838014, /*Answer for n = 37 is*/ 35548790, /*Answer for n = 38 is*/ 56153296, /*Answer for n = 39 is*/ 87640646, /*Answer for n = 40 is*/ 138180196, /*Answer for n = 41 is*/ 216065986, /*Answer for n = 42 is*/ 340223834, /*Answer for n = 43 is*/ 532680994, /*Answer for n = 44 is*/ 838025410, /*Answer for n = 45 is*/ 1313251780, /*Answer for n = 46 is*/ };
*Edited by author 31.12.2019 16:33* Re: Sheer bliss! Thanks for the sequence! The problem is indeed solved with linear recurrence (your message from 2012). Although, it seems k=20 here, and one needs to run Gauss on 20x20 matrix. I got by solution by using Berlekamp—Massey though. I wonder, how could you guess there is a linear recurrence and that K is small enough to brute force the sequence in finite time (I assume that's how you got it).
*Edited by author 31.12.2019 18:41* |