A213772 Principal diagonal of the convolution array A213771.

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

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