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Search: id:A101362
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| 0, 2, 48, 324, 1280, 3750, 9072, 19208, 36864, 65610, 110000, 175692, 269568, 399854, 576240, 810000, 1114112, 1503378, 1994544, 2606420, 3360000, 4278582, 5387888, 6716184, 8294400, 10156250, 12338352, 14880348, 17825024, 21218430
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OFFSET
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0,2
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COMMENT
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(n+1)*(n^4) + 6*Sum[i=1,n][i^3] + 4*Sum[i=1,n][i^2] + Sum[i=1,n][i] = 5*Sum[i=1,n][i^4].
For n>=4, a(n-1) is equal to the number of functions f:{1,2,3,4,5}->{1,2,...,n} such that for fixed, different x_1, x_2, x_3, x_4 in {1,2,3,4,5} and fixed y_1, y_2, y_3, y_ 4 in {1,2,...n} we have f(x_i)<>y_i, (i=1,2,3,4). - Milan R. Janjic (agnus(AT)blic.net), May 13 2007
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REFERENCES
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K. Kanim, "Proof Without Words", Mathematics Magazine, Vol. 77, No. 4 (2004), pp. 298-299.
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LINKS
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Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
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EXAMPLE
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a(5) = (5+1)*5^4 = 3750 = 2 * 3 * 5^4, the sum of the divisors of which is 30008.
a(7) = 8*7^4 = 19208 = 2^3 * 7^4 = 98^2 + 98^2.
a(8) = 9*8^4 = 36864 = 2^12*3^2 = 192^2.
a(9) = 10*9^4 = 65610 = 2*3^8*5 = 243^2 + 81^2.
a(10) = 11*10^4 = 110000 = 2^4*5^4*11 = 300^2 + 100^2 + 100^2.
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MATHEMATICA
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Table[(n + 1)*n^4, {n, 0, 30}]
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CROSSREFS
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Adjacent sequences: A101359 A101360 A101361 this_sequence A101363 A101364 A101365
Sequence in context: A087259 A083251 A075690 this_sequence A058090 A051252 A005429
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Dec 25 2004
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EXTENSIONS
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Corrected and extended by Chandler (rayjchandler(AT)sbcglobal.net), Dec 26, 2004
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