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Search: id:A065113
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| A065113 |
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Sum of the squares of the n-th and the n+1_st triangular numbers (A000217) is a perfect square. |
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+0
2
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| 6, 40, 238, 1392, 8118, 47320, 275806, 1607520, 9369318, 54608392, 318281038, 1855077840, 10812186006, 63018038200, 367296043198, 2140758220992, 12477253282758, 72722761475560, 423859315570606, 2470433131948080
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The sequence of square roots of the sum of the squares of the n-th and the n+1_th triangular numbers is A046176.
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FORMULA
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2 * A001652 = -1 + A002315 = a(n+1) - A003499(n+1).
G.f.: 2x(3-x)/((1-6x+x^2)(1-x)). a(n)=6a(n-1)-a(n-2)+4. a(-1-n)=-a(n)-2. - Michael Somos, Apr 07 2003
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EXAMPLE
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T6 = 21 and T7 = 28, 21^2 + 28^2 = 441 + 784 = 1225 = 35^2
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MATHEMATICA
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CoefficientList[ Series[2*(x - 3)/(-1 + 7x - 7x^2 + x^3), {x, 0, 24} ], x]
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PROGRAM
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(PARI) a(n)=-1+subst(poltchebi(abs(n+1))-poltchebi(abs(n)), x, 3)/2
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CROSSREFS
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a(n) = 2 A001652(n) = A002315(n)-1. A003499(n)=a(n)-a(n-1). Cf. A065651.
Sequence in context: A055344 A059021 A026077 this_sequence A052518 A135032 A122074
Adjacent sequences: A065110 A065111 A065112 this_sequence A065114 A065115 A065116
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 12 2001
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