A096979 Sum of the areas of the first n+1 Pell triangles.

0, 1, 6, 36, 210, 1225, 7140, 41616, 242556, 1413721, 8239770, 48024900, 279909630, 1631432881, 9508687656, 55420693056, 323015470680, 1882672131025, 10973017315470, 63955431761796, 372759573255306, 2172602007770041

Offset

0,3

Comments

Convolution of A059841(n) and A001109(n+1).

Partial sums of A084158.

Links

Table of n, a(n) for n=0..21.

S. Falcon, On the Sequences of Products of Two k-Fibonacci Numbers, American Review of Mathematics and Statistics, March 2014, Vol. 2, No. 1, pp. 111-120.

Roger B. Nelson, Multi-Polygonal Numbers, Mathematics Magazine, Vol. 89, No. 3 (June 2016), pp. 159-164.

Index entries for linear recurrences with constant coefficients, signature (6,0,-6,1).

Formula

G.f.: x/((1-x)*(1+x)*(1-6*x+x^2)).

a(n) = 6*a(n-1)-6*a(n-3)+a(n-4).

a(n) = (3-2*sqrt(2))^n*(3/32-sqrt(2)/16)+(3+2*sqrt(2))^n*(sqrt(2)/16+3/32)-(-1)^n/16-1/8.

a(n) = sum{k=0..n, (sqrt(2)*(sqrt(2)+1)^(2*k)/8-sqrt(2)*(sqrt(2)-1)^(2*k)/8)*((1+(-1)^(n-k))/2.

a(n) = sum{k=0..n, A001029(k)*A001029(k+1)/2}.

a(n) = (A001333(n+1)^2 - 1)/8 = ((A000129(n) + A000129(n+1))^2 - 1)/8. - Richard R. Forberg, Aug 25 2013

a(n) = A002620(A000129(n+1)) = A000217(A048739(n-1)), n > 0. - Ivan N. Ianakiev, Jun 21 2014

Mathematica

Accumulate[LinearRecurrence[{5, 5, -1}, {0, 1, 5}, 30]] (* Harvey P. Dale, Sep 07 2011 *)
LinearRecurrence[{6, 0, -6, 1}, {0, 1, 6, 36}, 22] (* Ray Chandler, Aug 03 2015 *)

Crossrefs

Cf. A096977, A064831, A096978.

Sequence in context: A269603 A027910 A075848 * A269464 A123887 A358539

Adjacent sequences: A096976 A096977 A096978 * A096980 A096981 A096982

Keyword

easy,nonn

Author

Paul Barry, Jul 17 2004

Status

approved