A074878 Row sums of triangle in A074829.

1, 2, 6, 14, 32, 70, 150, 316, 658, 1358, 2784, 5678, 11534, 23356, 47178, 95110, 191440, 384854, 772902, 1550972, 3110306, 6234142, 12490176, 25015774, 50088862, 100270460, 200690970, 401624726, 803642288, 1607920198, 3216868854, 6435401788, 12873496114, 25751348846

Offset

1,2

Comments

An elephant sequence, see A175654. For the corner squares 16 A[5] vectors, with decimal values between 43 and 424, lead to this sequence. For the central square these vectors lead to the companion sequence A175657. - Johannes W. Meijer, Aug 15 2010

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3,-1,-2).

Formula

From Philippe Deléham, Sep 20 2006: (Start)

a(1)=1, a(2)=2, a(3)=6, a(n) = 3*a(n-1) - a(n-2) - 2*a(n-3) for n>3.

a(n) = 3*2^(n-1) - 2*F(n+1), F(n)=A000045(n).

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

a(1)=1, a(n) = 2*(a(n-1) + F(n-2)) where the Fibonacci number F(n-2) = A000045(n-2). - Anton Vrba (antonvrba(AT)yahoo.com), Feb 06 2007

a(n) = 3*2^n - 2*F(n+2), with offset 0 and F(n)=A000045(n). - Johannes W. Meijer, Aug 15 2010

Mathematica

Table[3*2^(n-1) - 2*Fibonacci[n+1], {n, 1, 40}] (* G. C. Greubel, Jul 12 2019 *)

Prog

(PARI) vector(40, n, 3*2^(n-1) -2*fibonacci(n+1)) \\ G. C. Greubel, Jul 12 2019
(Magma) [3*2^(n-1) - 2*Fibonacci(n+1): n in [1..40]]; // G. C. Greubel, Jul 12 2019
(Sage) [3*2^(n-1) - 2*fibonacci(n+1) for n in (1..40)] # G. C. Greubel, Jul 12 2019
(GAP) List([1..40], n-> 3*2^(n-1) - 2*Fibonacci(n+1)); # G. C. Greubel, Jul 12 2019

Crossrefs

Cf. A000045.

Sequence in context: A346679 A232434 A096238 * A065495 A131352 A232230

Adjacent sequences: A074875 A074876 A074877 * A074879 A074880 A074881

Keyword

easy,nonn

Author

Joseph L. Pe, Sep 30 2002

Extensions

More terms from Philippe Deléham, Sep 20 2006

Terms a(23) onward added by G. C. Greubel, Jul 12 2019

Status

approved