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A074878
Row sums of triangle in A074829.
7
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
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
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