A012814 Take every 5th term of Padovan sequence A000931, beginning with the third term.
0, 1, 5, 21, 86, 351, 1432, 5842, 23833, 97229, 396655, 1618192, 6601569, 26931732, 109870576, 448227521, 1828587033, 7459895657, 30433357674, 124155792775, 506505428836, 2066337330754, 8429820731201, 34390259761825, 140298353215075, 572360547759276, 2334999585697905
Offset: 0
Examples
G.f. = x + 5*x^2 + 21*x^3 + 86*x^4 + 351*x^5 + 1432*x^6 + 5842*x^7 + ...
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Ulrich Brenner, Anna Hermann, and Jannik Silvanus, Constructing Depth-Optimum Circuits for Adders and AND-OR Paths, arXiv:2012.05550 [cs.DM], 2020.
- Sela Fried, Even-up words and their variants, arXiv:2505.14196 [math.CO], 2025. See p. 7.
- Taras Goy and Mark Shattuck, Toeplitz-Hessenberg determinant formulas for the sequence F_n-1, Online J. Anal. Comb. 19 (2024), no. 19, Paper #1, 27 pp. See Theorem 3.1.
- Index entries for linear recurrences with constant coefficients, signature (5,-4,1).
Programs
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Magma
I:=[0, 1, 5 ]; [n le 3 select I[n] else 5*Self(n-1)-4*Self(n-2)+Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 03 2012
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Mathematica
LinearRecurrence[{5, -4, 1}, {0, 1, 5}, 25] (* Vincenzo Librandi, Feb 03 2012 *)
Formula
a(n+3) = 5*a(n+2) - 4*a(n+1) + a(n).
a(n) = A000931(5*n+2).
G.f.: x/(1-5*x+4*x^2-x^3). - Colin Barker, Feb 03 2012
Extensions
Initial term 0 added by Colin Barker, Feb 03 2012