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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 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 EXTENSIONS Corrected by T. D. Noe, Nov 08 2006 STATUS approved

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Last modified June 21 11:18 EDT 2021. Contains 345362 sequences. (Running on oeis4.)