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Search: id:A166943
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| A166943 |
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One third of product plus sum of six consecutive nonnegative numbers. |
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+0
4
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| 5, 247, 1689, 6731, 20173, 50415, 110897, 221779, 411861, 720743, 1201225, 1921947, 2970269, 4455391, 6511713, 9302435, 13023397, 17907159, 24227321, 32303083, 42504045, 55255247, 71042449, 90417651, 114004853, 142506055
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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a(n) = ((n*...*(n+5))+(n+...+(n+5)))/3, n >= 0.
Binomial transform of 5, 242, 1200, 2400, 2400, 1200, 240, 0, 0, 0, 0, ....
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FORMULA
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a(n) = (n^6 + 15n^5 + 85n^4 + 225n^3 + 274n^2 + 126n + 15)/3. [From Charles R Greathouse IV (charles.greathouse(AT)case.edu), Nov 04 2009]
a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6)+240 for n > 5; a(0)=5, a(1)=247, a(2)=1689, a(3)=6731, a(4)=20173, a(5)=50415. [From Klaus Brockhaus, Nov 14 2009]
G.f.: (5+212*x+65*x^2-80*x^3+55*x^4-20*x^5+3*x^6)/(1-x)^7. [From Klaus Brockhaus, Nov 14 2009]
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EXAMPLE
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a(0) = (0*1*2*3*4*5+0+1+2+3+4+5)/3 = (0+15)/3 = 5.
a(1) = (1*2*3*4*5*6+1+2+3+4+5+6)/3 = (720+21)/3 = 247.
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MATHEMATICA
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lst={}; Do[p=(n+5)*(n+4)*(n+3)*(n+2)*(n+1)*n+(n+5)+(n+4)+(n+3)+(n+2)+(n+1)+n; AppendTo[lst, p/3], {n, 0, 5!}]; lst
(Plus@@#+Times@@#)/3&/@Partition[Range[0, 30], 6, 1] [From Harvey Dale (hpd1(AT)nyu.edu), Nov 10 2009]
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PROGRAM
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(MAGMA) [ (&*s + &+s)/3 where s is [n..n+5]: n in [0..25] ]; [From Klaus Brockhaus, Nov 14 2009]
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CROSSREFS
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Cf. A001477 (nonnegative integers), A028387 (n+(n+1)^2), A167875, A166941, A166942.
Adjacent sequences: A166940 A166941 A166942 this_sequence A166944 A166945 A166946
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KEYWORD
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nonn,easy,new
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AUTHOR
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Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 24 2009
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EXTENSIONS
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Edited and offset corrected by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 14 2009
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