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Search: id:A059270
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| A059270 |
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Numbers which are both the sum of n+1 consecutive integers and the sum of the n immediately higher consecutive integers. |
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4
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| 0, 3, 15, 42, 90, 165, 273, 420, 612, 855, 1155, 1518, 1950, 2457, 3045, 3720, 4488, 5355, 6327, 7410, 8610, 9933, 11385, 12972, 14700, 16575, 18603, 20790, 23142, 25665, 28365, 31248, 34320, 37587, 41055, 44730, 48618, 52725, 57057, 61620
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Group the non-multiples of n as follows e.g. for n = 4 (1,2,3),(5,6,7),(9,10,11),(13,14,15),... Then a(n) = the sum of the members of the n-th group. Or, the sum of (n-1)successive numbers preceding n^2. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jan 19 2004
Convolution of odds (A005408) and multiples of three (A008585) - Graeme McRae (g_m(AT)mcraefamily.com), Jun 06 2006
Sums of rows of the triangle in A126890. - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Dec 30 2006
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FORMULA
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a(n) = n(n+1)(2n+1)/2 = A000330(n)*3 = A006331(n)*3/2 = A055112(n)/2 = A000217(A002378(n))-A000217(A005563(n-1)) = A000217(A005563(n))-A000217(A002378(n))
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EXAMPLE
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a(5)=25+26+27+28+29+30=31+32+33+34+35=165
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MAPLE
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a:=n->sum((n^2+j), j=0..n): seq(a(n), n=0..39); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 27 2006
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CROSSREFS
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Sum of i from i=n^2 (A000290) through to n^2+n (A002378) and from i=n^2+n+1 (A002061 offset) through to n^2+2n (A005563). Cf. A059255 for analogue for sum of squares.
a(n) = A110449(n+1,n-1) for n>1.
Adjacent sequences: A059267 A059268 A059269 this_sequence A059271 A059272 A059273
Sequence in context: A012256 A012222 A069267 this_sequence A093627 A101165 A127407
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KEYWORD
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easy,nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Jan 24 2001
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