A134638 Row sums of triangle A134637.

1, 8, 28, 76, 182, 406, 868, 1808, 3706, 7522, 15176, 30508, 61198, 122606, 245452, 491176, 982658, 1965658, 3931696, 7863812, 15728086, 31456678, 62913908, 125828416, 251657482, 503315666, 1006632088, 2013264988, 4026530846, 8053062622, 16106126236

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2).

Formula

Binomial transform of [1, 7, 13, 15, 15, 15, ...].

G.f. x*(1+3*x-3*x^2+x^3) / ( (2*x-1)*(x-1)^3 ). - R. J. Mathar, Apr 04 2012

From Colin Barker, Nov 04 2017: (Start)

a(n) = -8 + 15*2^(n-1) - 5*n - n^2.

a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4) for n>4.

(End)

Example

a(3) = 28 = sum of row 3 terms of triangle A134637: 10 + 8 + 10.
a(3) = 28 = (1, 2, 1) dot (1, 8, 28) = (1 + 14 + 13).

Mathematica

LinearRecurrence[{5, -9, 7, -2}, {1, 8, 28, 76}, 40] (* Harvey P. Dale, Feb 24 2018 *)

Prog

(PARI) Vec(x*(1 + 3*x - 3*x^2 + x^3) / ((1 - x)^3*(1 - 2*x)) + O(x^40)) \\ Colin Barker, Nov 04 2017

Crossrefs

Cf. A134637.

Sequence in context: A212565 A209408 A316214 * A293289 A305638 A331757

Adjacent sequences: A134635 A134636 A134637 * A134639 A134640 A134641

Keyword

nonn,easy

Author

Gary W. Adamson, Nov 04 2007

Extensions

Corrected by R. J. Mathar, Apr 04 2012

Status

approved