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A131328
Row sums of triangle A131327.
2
1, 4, 5, 12, 17, 32, 49, 84, 133, 220, 353, 576, 929, 1508, 2437, 3948, 6385, 10336, 16721, 27060, 43781, 70844, 114625, 185472, 300097, 485572, 785669, 1271244, 2056913, 3328160, 5385073, 8713236, 14098309, 22811548, 36909857, 59721408, 96631265, 156352676
OFFSET
0,2
COMMENTS
a(n)/a(n-1) tends to phi. (Cf. A062114).
FORMULA
a(n+1) = A131326(n) + A052952(n+1).
a(n) = -3*(1+(-1)^n)/2 +4*A000045(n+1). - R. J. Mathar, Aug 13 2012
G.f.: ( 1+3*x-x^2 ) / ( (x-1)*(1+x)*(x^2+x-1) ). - R. J. Mathar, Aug 13 2012
From Colin Barker, Jul 12 2017: (Start)
a(n) = (2^(1-n)*((1+sqrt(5))^(n+1) - (1-sqrt(5))^(n+1))) / sqrt(5) - 3 for n even.
a(n) = (2^(1-n)*((1+sqrt(5))^(n+1) - (1-sqrt(5))^(n+1))) / sqrt(5) for n odd.
a(n) = a(n-1) + 2*a(n-2) - a(n-3) - a(n-4) for n>3.
(End)
EXAMPLE
a(3) = 12 = sum of row 3 terms of A131327: (3 + 5 + 3 + 1).
a(3) = (9 + 3) since we add terms of A131326: (1, 3, 4, 9, 13,...) to A052952: (0, 1, 1, 3, 4,...), getting (9 + 3 ) = 12.
PROG
(PARI) Vec((1 + 3*x - x^2) / ((1 - x)*(1 + x)*(1 - x - x^2)) + O(x^50)) \\ Colin Barker, Jul 12 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Jun 28 2007
EXTENSIONS
More terms from Colin Barker, Jul 12 2017
STATUS
approved