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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n)/a(n-1) tends to phi. (Cf. A062114).

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,2,-1,-1).

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

Cf. A062114, A052952, A131324, A131325, A131326, A131327.

Sequence in context: A103650 A131116 A261692 * A054451 A309479 A308775

Adjacent sequences:  A131325 A131326 A131327 * A131329 A131330 A131331

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Jun 28 2007

EXTENSIONS

More terms from Colin Barker, Jul 12 2017

STATUS

approved

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Last modified January 17 20:36 EST 2020. Contains 330987 sequences. (Running on oeis4.)