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A053221 Row sums of triangle A053218. 6
1, 5, 16, 43, 106, 249, 568, 1271, 2806, 6133, 13300, 28659, 61426, 131057, 278512, 589807, 1245166, 2621421, 5505004, 11534315, 24117226, 50331625, 104857576, 218103783, 452984806, 939524069, 1946157028, 4026531811, 8321499106 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Considered as a vector, the sequence = A074909 * [1, 2, 3,...], where A074909 is the beheaded Pascal's triangle as a matrix. - Gary W. Adamson, Mar 06 2012

a(n) is the sum of the upper left n X n subarray of A052509 (viewed as an infinite square array). For example (1+1+1) + (1+2+2) + (1+3+4) = 16. - J. M. Bergot, Nov 06 2012

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..3311

Index entries for linear recurrences with constant coefficients, signature (6,-13,12,-4).

FORMULA

a(n) = (n+2)*2^(n-1)-n-1. - Vladeta Jovovic, Feb 28 2003

G.f. -x*(-1+x+x^2) / ( (2*x-1)^2*(x-1)^2 ). - R. J. Mathar, Sep 02 2011

a(n) = (1/2) * Sum_{k=1..n} Sum_{i=1..n} C(k,i) + C(n,k). - Wesley Ivan Hurt, Sep 22 2017

EXAMPLE

a(4) = 4 + 7 + 12 + 20 = 43.

MAPLE

A053221 := proc(n) (n+2)*2^(n-1)-n-1 ; end proc: # R. J. Mathar, Sep 02 2011

MATHEMATICA

Table[(n + 2)*2^(n - 1) - n - 1, {n, 29}] (* or *)

Rest@ CoefficientList[Series[-x (-1 + x + x^2)/((2 x - 1)^2*(x - 1)^2), {x, 0, 29}], x] (* Michael De Vlieger, Sep 22 2017 *)

PROG

(PARI) vector(50, n, (n+2)*2^(n-1)-n-1) \\ G. C. Greubel, Sep 03 2018

(MAGMA) [(n+2)*2^(n-1)-n-1: n in [1..50]]; // G. C. Greubel, Sep 03 2018

CROSSREFS

Cf. A053218, A053219, A053220.

Cf. A074909.

Sequence in context: A241794 A034358 A036888 * A137221 A137234 A271359

Adjacent sequences:  A053218 A053219 A053220 * A053222 A053223 A053224

KEYWORD

nonn,easy

AUTHOR

Asher Auel (asher.auel(AT)reed.edu), Jan 01 2000

STATUS

approved

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Last modified July 17 18:41 EDT 2019. Contains 325109 sequences. (Running on oeis4.)