A213837 Principal diagonal of the convolution array A213836.

1, 13, 52, 134, 275, 491, 798, 1212, 1749, 2425, 3256, 4258, 5447, 6839, 8450, 10296, 12393, 14757, 17404, 20350, 23611, 27203, 31142, 35444, 40125, 45201, 50688, 56602, 62959, 69775, 77066, 84848, 93137

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) = n*(5 - 15*n + 16*n^2)/6.

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

G.f.: f(x)/g(x), where f(x) = x*(1 + 9*x + 6*x^2) and g(x) = (1-x)^4.

a(n) = n*A002412(n) - (n-1)*A002412(n-1). [Bruno Berselli, Dec 11 2012]

a(n) = n*A000384(n) + sum( A000384(i), i=0..n-1 ). [Bruno Berselli, Dec 18 2013]

Mathematica

(See A213836.)

Crossrefs

Cf. A000384, A002412, A213836, 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).

Sequence in context: A183941 A022673 A152742 * A047903 A197790 A317467

Adjacent sequences: A213834 A213835 A213836 * A213838 A213839 A213840

Keyword

nonn,easy

Author

Clark Kimberling, Jul 04 2012

Status

approved