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A048776 First partial sums of A048739; second partial sums of A000129. 9
1, 4, 12, 32, 81, 200, 488, 1184, 2865, 6924, 16724, 40384, 97505, 235408, 568336, 1372096, 3312545, 7997204, 19306972, 46611168, 112529329, 271669848, 655869048, 1583407968, 3822685009, 9228778012, 22280241060, 53789260160, 129858761409, 313506783008 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..29.

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

FORMULA

a(n) = 2*a(n-1) + a(n-2) + n + 1; a(0)=1, a(1)=4.

a(n) = (((7/2 + (5/2)*sqrt(2))*(1+sqrt(2))^n - (7/2 - (5/2)*sqrt(2))*(1-sqrt(2))^n)/2*sqrt(2)) - (n+3)/2.

a(n) = (A000129(n+3) - (n+3))/2 = Sum_{j} A047662(n-j+1, j+1). - Henry Bottomley, Jul 09 2001

From R. J. Mathar, Feb 06 2010: (Start)

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

G.f.: -1/((x^2+2*x-1) * (x-1)^2). (End)

Define an array with m(n,1)=1 and m(1,k) = k*(k+1)/2 for n=1,2,3,...  The interior terms are m(n,k) = m(n,k-1) + m(n-1,k-1) + m(n-1,k). The sum of the terms in each antidiagonal=a(n). - J. M. Bergot, Dec 01 2012 [This is A154948 without the first column. The diagonal is m(n,n) = A161731(n-1). R. J. Mathar, Dec 06 2012]

MAPLE

with(combinat):seq((fibonacci(n, 2)-n)/2, n=3..25); # Zerinvary Lajos, Jun 02 2008

MATHEMATICA

a=b=0; Table[c=2*b+a+n; a=b; b=c, {n, 1, 40}] (* Vladimir Joseph Stephan Orlovsky, Apr 02 2011*)

LinearRecurrence[{4, -4, 0, 1}, {1, 4, 12, 32}, 30] (* Harvey P. Dale, Aug 27 2014 *)

CROSSREFS

Cf. A001333, A000129, A048739.

Sequence in context: A001787 A118442 A038592 * A135248 A205976 A291038

Adjacent sequences:  A048773 A048774 A048775 * A048777 A048778 A048779

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams

EXTENSIONS

More terms from Harvey P. Dale, Aug 27 2014

STATUS

approved

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Last modified September 17 18:50 EDT 2019. Contains 327136 sequences. (Running on oeis4.)