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A098156
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Interleave n+1 and 2n+1 and take binomial transform.
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6
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1, 2, 5, 13, 32, 76, 176, 400, 896, 1984, 4352, 9472, 20480, 44032, 94208, 200704, 425984, 901120, 1900544, 3997696, 8388608, 17563648, 36700160, 76546048, 159383552, 331350016, 687865856, 1426063360, 2952790016, 6106906624
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OFFSET
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0,2
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COMMENTS
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An elephant sequence, see A175655. For the central square 16 A[5] vectors, with decimal values between 59 and 440, lead to this sequence (without a(1)). For the corner squares these vectors lead to the companion sequence A066373 (with a leading 1 added). - Johannes W. Meijer, Aug 15 2010
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LINKS
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FORMULA
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G.f.: (1-2*x+x^2+x^3)/(1-2*x)^2.
a(n) = (2 * 0^n + Sum_{k=0..n} (-1)^(n-k)*k*binomial(n,k) + 2^(n+1) + 3*n*2^(n-1) )/4.
a(n) = Sum_{j=0..n} Sum_{k=0..n} binomial(n, 2*(k-j)).
a(n) = Sum_{k=0..n} Sum_{j=0..k} C(n, 2*j). - Paul Barry, Jan 13 2005
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MATHEMATICA
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CoefficientList[Series[(1-2x+x^2+x^3)/(1-2x)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Jul 21 2013 *)
LinearRecurrence[{4, -4}, {1, 2, 5, 13}, 50] (* Harvey P. Dale, Dec 03 2023 *)
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PROG
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(PARI) {a(n) = if(n==0, 1, if(n==1, 2, 2^(n-3)*(3*n+4)))}; \\ G. C. Greubel, May 08 2019
(Magma) [1, 2] cat [2^(n-3)*(3*n+4): n in [2..40]]; // G. C. Greubel, May 08 2019
(Sage) [1, 2]+[2^(n-3)*(3*n+4) for n in (2..40)] # G. C. Greubel, May 08 2019
(GAP) Concatenation([1, 2], List([2..40], n-> 2^(n-3)*(3*n+4))) # G. C. Greubel, May 08 2019
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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