A223940 Sums of antidiagonals of A223968.

1, 2, 4, 8, 16, 31, 61, 117, 228, 436, 845, 1615, 3120, 5965, 11501, 22001, 42365, 81091, 156010, 298777, 574450, 1100620, 2115150, 4053959, 7788126, 14931102, 28676899, 54990202, 105594073, 202519004, 388825095, 745825185, 1431776536, 2746639052

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,4,-3,-3,1).

Formula

G.f.: (1-x) * (1+2*x-x^3) / (1-x-4*x^2+3*x^3+3*x^4-x^5).

a(n) = a(n-1) + 4*a(n-2) - 3*a(n-3) - 3*a(n-4) + a(n-5) with a(0) = 1, a(1) = 2, a(2) = 4, a(3) = 8, a(4) = 16, a(5) = 31.

a(n) = Sum_{k=0..n} A223968(n-k, k).

Mathematica

CoefficientList[Series[(1-x)(1+2x-x^3)/(1-x-4x^2+3x^3+3x^4-x^5), {x, 0, 40}], x] (* or *) LinearRecurrence[{1, 4, -3, -3, 1}, {1, 2, 4, 8, 16}, 40] (* Harvey P. Dale, Jul 04 2019 *)

Crossrefs

Cf. A223968

Sequence in context: A347776 A006775 A104993 * A189076 A192656 A128761

Adjacent sequences: A223937 A223938 A223939 * A223941 A223942 A223943

Keyword

nonn,easy

Author

Philippe Deléham, Mar 29 2013

Extensions

a(32) corrected by Sean A. Irvine, May 19 2019

Status

approved