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Search: id:A094706
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| A094706 |
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Convolution of Pell(n) and 2^n. |
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+0
4
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| 0, 1, 4, 13, 38, 105, 280, 729, 1866, 4717, 11812, 29365, 72590, 178641, 438064, 1071153, 2613138, 6362965, 15470140, 37565389, 91125206, 220864377, 534951112, 1294960905, 3133261530, 7578261181, 18323338324, 44292046693, 107041649438
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n) = sum of n-th row in A101164 = A000129(n)-A000079(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 03 2004
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FORMULA
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G.f. : x/((1-2x-x^2)(1-2x)); a(n)=sum{k=0..n, ((1+sqrt(2))^n-(1-sqrt(2))^n)/(2sqrt(2))2^(n-k)}; a(n)=(1+sqrt(2))^n(1+3sqrt(2)/4)+(1-sqrt(2))^n(1-3sqrt(2)/4)-2^(n+1); a(n)=4a(n-1)-3a(n-2)-2a(n-3).
a(n)=sum{k=0..floor(n/2), binomial(n-k, k+1)2^(n-2k-1)}; a(n)=sum{k=0..n, binomial(k, n-k+1)2^k*(1/2)^(n-k+1)}. - Paul Barry (pbarry(AT)wit.ie), Oct 07 2004
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CROSSREFS
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Cf. A000129, A000079.
Sequence in context: A089092 A049611 A084851 this_sequence A056014 A159036 A058693
Adjacent sequences: A094703 A094704 A094705 this_sequence A094707 A094708 A094709
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), May 21 2004
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