login
A132738
Row sums of triangle A132737.
2
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
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
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Aug 26 2007
EXTENSIONS
Extended by Franklin T. Adams-Watters, Jul 06 2009
STATUS
approved