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

Author

Joseph L. Pe, Sep 30 2002

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A000045.

Programs

GAP

List([1..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

Mathematica

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

PARI

vector(40, n, 3*2^(n-1) -2*fibonacci(n+1)) \\ 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

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

Extensions

More terms from Philippe Deléham, Sep 20 2006

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