A131913 Product of the square matrix in A065941 and the column vector (1, 2, 3, ...)'.

1, 3, 6, 13, 25, 48, 89, 163, 294, 525, 929, 1632, 2849, 4947, 8550, 14717, 25241, 43152, 73561, 125075, 212166, 359133, 606721, 1023168, 1722625, 2895843, 4861254, 8149933, 13646809, 22825200, 38136089, 63653827, 106146534, 176849517, 294401825, 489706272

Offset

0,2

Links

Table of n, a(n) for n=0..35.

Index entries for linear recurrences with constant coefficients, signature (2,1,-2,-1).

Formula

Equals A010049(n) + A001629(n+2) and A055244(n) + A001629(n-1).

From Philippe Deléham, Dec 28 2013: (Start)

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

a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) - a(n-4), a(0)=1, a(1)=3, a(2)=6, a(3)=13.

a(n) = a(n-1) + a(n-2) + 2*Fibonacci(n). (End)

Example

a(4) = 25 = (1, 1, 3, 2, 1) dot (1, 2, 3, 4, 5) = (1 + 2 + 9 + 8 + 5), where (1, 1, 3, 2, 1) = row 4 of triangle A065941.
a(4) = 25 = A010049(4) + A001629(6) = 5 + 20.
a(5) = 48 = A055244(6) + A001619(4) = 43 + 5.

Crossrefs

Cf. A000045, A065941, A010049, A001629, A005244.

Sequence in context: A047194 A048039 A339617 * A182808 A285461 A324129

Adjacent sequences: A131910 A131911 A131912 * A131914 A131915 A131916

Keyword

nonn,easy

Author

Gary W. Adamson, Jul 27 2007

Status

approved