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A172173 Sums of NE-SW diagonals of triangle A172171. 1
0, 1, 1, 11, 12, 32, 44, 85, 129, 223, 352, 584, 936, 1529, 2465, 4003, 6468, 10480, 16948, 27437, 44385, 71831, 116216, 188056, 304272, 492337, 796609, 1288955, 2085564, 3374528, 5460092, 8834629, 14294721, 23129359, 37424080, 60553448, 97977528, 158530985 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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

For n=even: a(n) = a(n-1)+a(n-2); for n=odd: a(n) = a(n-1)+a(n-2)+9 ; with a(0)=0 and a(1)=1.

From Colin Barker, Feb 18 2013: (Start)

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

G.f.: x*(8*x^2+1) / ((x-1)*(x+1)*(x^2+x-1)).

(End)

a(n) = (2^(-1-n)*(-45*((-2)^n+2^n) + (45-7*sqrt(5))*(1+sqrt(5))^n + (1-sqrt(5))^n*(45+7*sqrt(5)))) / 5. - Colin Barker, Jul 13 2017

MATHEMATICA

CoefficientList[Series[x*(8*x^2+1)/((x-1)*(x+1)*(x^2+x-1)), {x, 0, 50}], x] (* G. C. Greubel, Jul 13 2017 *)

PROG

(PARI) concat(0, Vec(x*(1 + 8*x^2) / ((1 - x)*(1 + x)*(1 - x - x^2)) + O(x^50))) \\ Colin Barker, Jul 13 2017

CROSSREFS

Cf. A172171, A000045, A172172.

Sequence in context: A221644 A022316 A136433 * A061760 A309631 A075559

Adjacent sequences:  A172170 A172171 A172172 * A172174 A172175 A172176

KEYWORD

nonn,easy

AUTHOR

Mark Dols, Jan 28 2010

EXTENSIONS

Offset corrected by Colin Barker, Feb 18 2013

STATUS

approved

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Last modified November 19 00:12 EST 2019. Contains 329310 sequences. (Running on oeis4.)