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A144707 Diagonal sums of Pascal-like triangle A132047. 1
1, 1, 2, 7, 11, 22, 35, 61, 98, 163, 263, 430, 695, 1129, 1826, 2959, 4787, 7750, 12539, 20293, 32834, 53131, 85967, 139102, 225071, 364177, 589250, 953431, 1542683, 2496118, 4038803, 6534925, 10573730, 17108659, 27682391, 44791054, 72473447, 117264505 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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

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

a(n) = 3*F(n+1) - 3 - (-1)^n + 2*0^n.

a(n) = a(n-1) + 2*a(n-2) - a(n-3) - a(n-4) for n>4. - Philippe Deléham, Dec 16 2008

From Colin Barker, Jul 12 2017: (Start)

a(n) = (3*2^(-n-1)*((1 + sqrt(5))^(n+1) - (1-sqrt(5))^(n+1))) / sqrt(5) - 4 for n>0 and even.

a(n) = (3*2^(-n-1)*((1+sqrt(5))^(n+1) - (1-sqrt(5))^(n+1)))/sqrt(5) - 2 for n odd.

(End)

PROG

(PARI) Vec((1-x^2+4*x^3+2*x^4) / ((1-x^2)*(1-x-x^2)) + O(x^50)) \\ Colin Barker, Jul 12 2017

CROSSREFS

Sequence in context: A103182 A160698 A294114 * A045373 A075431 A184799

Adjacent sequences:  A144704 A144705 A144706 * A144708 A144709 A144710

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Sep 19 2008

STATUS

approved

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Last modified March 30 06:59 EDT 2020. Contains 333119 sequences. (Running on oeis4.)