A263622 a(n) = (3^(n+1)-2^(n+2)+2*n+1)/4.
0, 1, 4, 14, 47, 153, 486, 1516, 4669, 14255, 43268, 130818, 394491, 1187557, 3570850, 10728920, 32219513, 96724059, 290303232, 871171822, 2614039735, 7843167761, 23531600414, 70598995524, 211805375157, 635432902663, 1906332262396, 5719063896026, 17157325905779, 51472246152765
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- H. Gupta, On a problem in parity, Indian J. Math., 11 (1969), 157-163. [Annotated scanned copy] See Q(w) on first page.
- Index entries for linear recurrences with constant coefficients, signature (7,-17,17,-6).
Programs
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PARI
a(n) = (3^(n+1)-2^(n+2)+2*n+1)/4 \\ Colin Barker, Oct 26 2015
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PARI
concat(0, Vec(x*(3*x^2-3*x+1)/((x-1)^2*(2*x-1)*(3*x-1)) + O(x^40))) \\ Colin Barker, Oct 26 2015
Formula
From Colin Barker, Oct 26 2015: (Start)
a(n) = 7*a(n-1)-17*a(n-2)+17*a(n-3)-6*a(n-4) for n>3.
G.f.: x*(3*x^2-3*x+1) / ((x-1)^2*(2*x-1)*(3*x-1)).
(End)
Extensions
Typo in last term fixed by Colin Barker, Oct 26 2015