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

Author

Philippe Deléham, Mar 29 2013

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A223968

Programs

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 *)

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).

Extensions

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