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A213824 Antidiagonal sums of the convolution array A213822. 3
4, 30, 114, 310, 690, 1344, 2380, 3924, 6120, 9130, 13134, 18330, 24934, 33180, 43320, 55624, 70380, 87894, 108490, 132510, 160314, 192280, 228804, 270300, 317200, 369954, 429030, 494914, 568110, 649140 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Every term is even.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

a(n) = (2*n + 5*n^2 + 6*n^3 + 3*n^4)/4 = n*(1 + n)*(2 + 3*n + 3*n^2)/4.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

G.f.: f(x)/g(x), where f(x) = 2*x*(2 + 5*x + 2*x^2) and g(x) = (1-x)^5.

a(n) = Sum_{i=1..n} i*(3*i^2+1). - Bruno Berselli, Feb 09 2017

MATHEMATICA

(See A213822.)

PROG

(PARI) a(n) = n*(3*n^3 + 6*n^2 + 5*n + 2)/4 \\ Charles R Greathouse IV, Feb 09 2017

CROSSREFS

Cf. A213822.

Sequence in context: A027297 A211628 A166761 * A333277 A027445 A027789

Adjacent sequences:  A213821 A213822 A213823 * A213825 A213826 A213827

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jul 04 2012

STATUS

approved

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Last modified May 7 12:52 EDT 2021. Contains 343650 sequences. (Running on oeis4.)