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A213763 Principal diagonal of the convolution array A213762. 3
1, 11, 43, 127, 331, 807, 1891, 4319, 9691, 21463, 47059, 102351, 221131, 475079, 1015747, 2162623, 4587451, 9699255, 20447155, 42991535, 90177451, 188743591, 394264483, 822083487, 1711275931, 3556769687, 7381974931 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Create a triangle with first column T(n,1)=1+4*n for n=0,1,2...   The remaining terms T(r,c)=T(r,c-1)+T(r-1,c-1).

The sum of the terms in row(n)=a(n+1). - J. M. Bergot, Dec 18 2012

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1000

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

FORMULA

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

a(n) = 6*a(n-1) - 13*a(n-2) + 12*a(n-3) - 4*a(n-4).

G.f.:  f(x)/g(x), where f(x) = x*(1 + 5*x - 10*x^2) and g(x) = (1 - 3*x + 2*x^2 )^2.

MATHEMATICA

(See A213762.)

LinearRecurrence[{6, -13, 12, -4}, {1, 11, 43, 127}, 30] (* Harvey P. Dale, Apr 13 2017 *)

CROSSREFS

Cf. A213762, A213500.

Sequence in context: A141086 A142039 A196153 * A302226 A201714 A269422

Adjacent sequences:  A213760 A213761 A213762 * A213764 A213765 A213766

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 20 2012

STATUS

approved

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Last modified August 12 12:01 EDT 2020. Contains 336439 sequences. (Running on oeis4.)