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A213772 Principal diagonal of the convolution array A213771. 5
1, 11, 42, 106, 215, 381, 616, 932, 1341, 1855, 2486, 3246, 4147, 5201, 6420, 7816, 9401, 11187, 13186, 15410, 17871, 20581, 23552, 26796, 30325, 34151, 38286, 42742, 47531, 52665, 58156, 64016, 70257, 76891 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

G.f.: x*(1 + 7*x + 4*x^2)/(1 - x)^4.

a(n) = (4*n^2-3*n+1)*n/2 = n*A002411(n) - (n-1)*A002411(n-1). [Bruno Berselli, Dec 11 2012]

a(n) = n*A000326(n) + sum( A000326(i), i=0..n-1 ). [Bruno Berselli, Dec 18 2013]

MATHEMATICA

(See A213771.)

PROG

(PARI) a(n) = (4*n^3-3*n^2+n)/2; \\ Altug Alkan, Dec 16 2017

CROSSREFS

Cf. A000326, A002411, A213771, A220084 (for a list of numbers of the form n*P(k,n)-(n-1)*P(k,n-1), where P(k,n) is the n-th k-gonal pyramidal number).

Cf. A260260 (comment). [Bruno Berselli, Jul 22 2015]

Sequence in context: A101985 A055437 A055436 * A062517 A027978 A050489

Adjacent sequences:  A213769 A213770 A213771 * A213773 A213774 A213775

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jul 04 2012

STATUS

approved

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Last modified October 21 11:42 EDT 2019. Contains 328296 sequences. (Running on oeis4.)