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A048778 First partial sums of A048745; second partial sums of A048654. 0
1, 6, 20, 56, 145, 362, 888, 2160, 5233, 12654, 30572, 73832, 178273, 430418, 1039152, 2508768, 6056737, 14622294, 35301380, 85225112, 205751665, 496728506, 1199208744, 2895146064, 6989500945, 16874148030, 40737797084, 98349742280, 237437281729, 573224305826, 1383885893472 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Define a triangle T by T(n,0)= n*(n+1)+1, T(n,n)= (n+1)*(n+2)/2, and T(r,c)= T(r-1,c) +T(r-1,c-1) +T(r-2,c-1). Then a(n) is the sum of row n. - J. M. Bergot, Mar 06 2013

LINKS

Table of n, a(n) for n=0..30.

Index entries for linear recurrences with constant coefficients, signature (4,-4,0,1)

FORMULA

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

a(n)=[ {(13/2+(9/2)*sqrt(2))(1+sqrt(2))^n - (13/2-(9/2)*sqrt(2))(1-sqrt(2))^n}/2*sqrt(2) ]-(3*n+7)/2.

G.f. ( -1-2*x ) / ( (x^2+2*x-1)*(x-1)^2 ). a(n) = A048776(n)+2*A048776(n-1). - R. J. Mathar, Nov 08 2012

PROG

(PARI)

N=66;  x='x+O('x^N);

gf= ( -1-2*x ) / ( (x^2+2*x-1)*(x-1)^2 );  Vec(Ser(gf))

/* Joerg Arndt, Mar 07 2013 */

CROSSREFS

Cf. A001333, A048745, A048654.

Sequence in context: A201149 A260777 A014480 * A048611 A292480 A200528

Adjacent sequences:  A048775 A048776 A048777 * A048779 A048780 A048781

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams

EXTENSIONS

Corrected by T. D. Noe, Nov 08 2006

STATUS

approved

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Last modified June 18 17:05 EDT 2019. Contains 324214 sequences. (Running on oeis4.)