A132738 Row sums of triangle A132737.

1, 2, 7, 16, 33, 66, 131, 260, 517, 1030, 2055, 4104, 8201, 16394, 32779, 65548, 131085, 262158, 524303, 1048592, 2097169, 4194322, 8388627, 16777236, 33554453, 67108886, 134217751, 268435480, 536870937, 1073741850, 2147483675, 4294967324, 8589934621

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Formula

Binomial transform of [1, 1, 4, 0, 4, 0, 4, ...].

a(n) = 2^(n+1) + n - 3 for n > 0. - Franklin T. Adams-Watters, Jul 06 2009

From Colin Barker, Mar 14 2014: (Start)

a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3) for n>3.

G.f.: (1 -2*x +4*x^2 -4*x^3)/((1-x)^2*(1-2*x)). (End)

E.g.f.: 2 - (3-x)*exp(x) + 2*exp(2*x). - G. C. Greubel, Feb 15 2021

Example

a(3) = 16 = sum of row 3 terms of triangle A132737: (1 + 7 + 7 + 1).
a(3) = 16 = (1, 3, 3, 1) dot (1, 1, 4, 0) = (1 + 3 + 12 + 0).

Mathematica

Join[{1, 2, 7}, Table[BitSet[n, (n+4)], {n, 0, 40}]] (* Vladimir Joseph Stephan Orlovsky, Jul 19 2011 *)
Table[2^(n+1) +n-3 +2*Boole[n==0], {n, 0, 40}] (* G. C. Greubel, Feb 15 2021 *)

Prog

(PARI) Vec((1-2*x+4*x^2-4*x^3)/((1-x)^2*(1-2*x)) + O(x^40)) \\ Colin Barker, Mar 14 2014
(Sage) [1]+[2^(n+1) +n-3 for n in (1..40)] # G. C. Greubel, Feb 15 2021
(Magma) [1] cat [2^(n+1) +n-3: n in [1..40]]; // G. C. Greubel, Feb 15 2021

Crossrefs

Cf. A132737.

Sequence in context: A208995 A023612 A192952 * A259966 A283500 A097442

Adjacent sequences: A132735 A132736 A132737 * A132739 A132740 A132741

Keyword

nonn,easy

Author

Gary W. Adamson, Aug 26 2007

Extensions

Extended by Franklin T. Adams-Watters, Jul 06 2009

Status

approved