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Search: id:A048395
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| A048395 |
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Sum of consecutive nonsquares. |
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+0
6
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| 0, 5, 26, 75, 164, 305, 510, 791, 1160, 1629, 2210, 2915, 3756, 4745, 5894, 7215, 8720, 10421, 12330, 14459, 16820, 19425, 22286, 25415, 28824, 32525, 36530, 40851, 45500, 50489, 55830, 61535, 67616, 74085, 80954, 88235, 95940, 104081
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Relationship with natural numbers: a(4) = (first term + last term)*n = (10+15)*3 = (25)*3 = 75; a(5) = (17+24)*4 = (41)4 = 164; ...
Also (X*Y*Z)/(X+Y+Z) of primitive Pythagorean triples (X,Y,Z=Y+1) as described in A046092 and A001844. - Lambert Herrgesell (zero815(AT)googlemail.com), Dec 13 2005
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LINKS
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Index entries for sequences related to sums of squares
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FORMULA
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a(n) = 2*n^3 + 2*n^2 + n.
sum ((n+j+2)^2-j^2+1,j=0..n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 13 2006
O.g.f.: x(x+5)(1+x)/(1-x)^4. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 12 2008
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EXAMPLE
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Between 3^2 and 4^2 we have 10+11+12+13+14+15 which is 75 or a(4).
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PROGRAM
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(PARI) v0=[1, 0, 1]; M=[1, 2, 2; -2, -1, -2; 2, 2, 3]; g(v)=v[1]*v[2]*v[3]/(v[1]+v[2]+v[3]); a(n)=g(v0*M^n); for(i=0, 50, print1(a(i), " ")) (Herrgesell)
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CROSSREFS
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Cf. A048396, A048397, A000027.
Cf. A048396, A048397, A000027, A046092, A001844.
Adjacent sequences: A048392 A048393 A048394 this_sequence A048396 A048397 A048398
Sequence in context: A049738 A042883 A139273 this_sequence A081886 A081530 A145013
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KEYWORD
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nonn,nice
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AUTHOR
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Patrick De Geest (pdg(AT)worldofnumbers.com), Mar 15 1999.
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