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A223940 Sums of antidiagonals of A223968. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A152718 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

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Last modified October 25 00:01 EDT 2020. Contains 338010 sequences. (Running on oeis4.)