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A181527 Binomial transform of A113127; (1, 1, 3, 7, 15, 31,...) convolved with (1, 3, 7, 15, 31, 63,...). 2
1, 4, 13, 38, 103, 264, 649, 1546, 3595, 8204, 18445, 40974, 90127, 196624, 426001, 917522, 1966099, 4194324, 8912917, 18874390, 39845911, 83886104, 176160793, 369098778, 771751963, 1610612764, 3355443229, 6979321886, 14495514655, 30064771104, 62277025825 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A181527 = Partial sums of (A002064 Cullen numbers: n*2^n+1) -- Vladimir Joseph Stephan Orlovsky, Jul 09 2011.

Form a triangle with T(1,1) = n, T(2,1) = T(2,2) = n-1, T(3,1) = T(3,3) = n-2, ..., T(n,1) = T(n,n) = 1.  The interior members are T(i,j) = T(i-1,j-1) + T(i-1,j).  The sum of all members for a triangle of size n is a(n-1).  Example for n = 5: row(1) = 5; row(2) = 4, 4; row(3) = 3, 8, 3; row(4) = 2, 11, 11, 2; row(5) = 1, 13, 22, 13, 1.  The sum of all members is 103 = a(4). - J. M. Bergot, Oct 16 2012

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (6,-13,12,-4). [From R. J. Mathar, Oct 30 2010]

FORMULA

Binomial transform of A113127; (1, 3, 7, 15, 31,...) convolved with

(1, 1, 3, 7, 15, 31,...).

EXAMPLE

a(4) = 103 = (1, 1, 3, 7, 15) dot (31, 15, 7, 3, 1) = (31 + 15 + 21, + 21 + 15)

a(3) = 38 = (1, 3, 3, 1) dot (1, 3, 6, 10) = (1 + 9 + 18 + 10).

a(n) = 3+n+ 2^(n+1)*(n-1) = 6*a(n-1) -13*a(n-2) +12*a(n-3) -4*a(n-4). G.f.: ( 1-2*x+2*x^2 ) / ( (2*x-1)^2*(x-1)^2 ). [From R. J. Mathar, Oct 30 2010]

MATHEMATICA

Accumulate[Table[n*2^n + 1, {n, 0, 60}]] (* Vladimir Joseph Stephan Orlovsky, Jul 09 2011 *)

LinearRecurrence[{6, -13, 12, -4}, {1, 4, 13, 38}, 40] (* Harvey P. Dale, Apr 14 2016 *)

CROSSREFS

Cf. A002064, A113127.

Sequence in context: A145128 A277974 A089092 * A049611 A084851 A094706

Adjacent sequences:  A181524 A181525 A181526 * A181528 A181529 A181530

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Oct 26 2010

STATUS

approved

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Last modified June 15 17:43 EDT 2019. Contains 324142 sequences. (Running on oeis4.)