A323227 a(n) = [x^n] (-x^4 + 2*x^3 - x^2 + 2*x - 1)/((x - 1)^2*(2*x - 1)).

1, 2, 4, 6, 9, 14, 23, 40, 73, 138, 267, 524, 1037, 2062, 4111, 8208, 16401, 32786, 65555, 131092, 262165, 524310, 1048599, 2097176, 4194329, 8388634, 16777243, 33554460, 67108893, 134217758, 268435487, 536870944, 1073741857, 2147483682, 4294967331, 8589934628

Offset

0,2

Links

Table of n, a(n) for n=0..35.

Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Formula

a(n) = Sum_{k=0..n} binomial(n - 2, k - 1) + 1 if n >= 2.

a(n) = ((2 - 2*n)*a(n-2) - (5 - 3*n)*a(n-1))/(n - 2) for n >= 4.

a(n+1) - (n + 1) = A094373(n) for n >= 0.

a(n+1) - a(n) = 2^n + 1 for n >= 2.

a(n) = A270841(n) = 2^(n-2)+n+1 for n>=2. - R. J. Mathar, Feb 14 2019

Maple

a := proc(n) option remember; if n < 4 then return [1, 2, 4, 6][n + 1] fi;
((2 - 2*n)*a(n-2) - (5 - 3*n)*a(n-1))/(n - 2) end: seq(a(n), n=0..35);

Mathematica

T[n_, k_] := If[n <= 1, 1, Binomial[n - 2, k - 1] + 1];
Table[Sum[T[n, k], {k, 0, n}], {n, 0, 35}]

Crossrefs

Cf. A000051, A094373.

Sequence in context: A164139 A218605 A024849 * A283024 A090483 A299494

Adjacent sequences: A323224 A323225 A323226 * A323228 A323229 A323230

Keyword

nonn,easy

Author

Peter Luschny, Feb 12 2019

Status

approved