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A140757
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Cumulative sums of A140756.
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1
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1, 0, 2, 3, 1, 4, 3, 5, 2, 6, 7, 5, 8, 4, 9, 8, 10, 7, 11, 6, 12, 13, 11, 14, 10, 15, 9, 16, 15, 17, 14, 18, 13, 19, 12, 20, 21, 19, 22, 18, 23, 17, 24, 16, 25, 24, 26, 23, 27, 22, 28, 21, 29, 20, 30, 31, 29, 32, 28, 33, 27, 34, 26, 35, 25, 36, 35, 37, 34, 38, 33, 39, 32, 40, 31, 41
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Each positive integer occurs exactly twice in this sequence, with 0 occurring only once. In particular, if A002620(n) < m < A002620(n+1), then m occurs in rows n-1 and n; and A002620(n) occurs in rows in rows n-1 (as T(n-1,n-1)) and n+1 (as T(n+1,n)).
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FORMULA
| G.f.: A(x) = x*(1+3*x^2+2*x^4)/((1-x)^2*(1-x^2)^2) - Paul D. Hanna (pauldhanna(AT)juno.com) T(n,k) = floor((n+(-1)^{n-k})^2/4) - (-1)^{n-k}*floor((n-k)/2)
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PROG
| (PARI) T(n, k)=if((n-k)%2==0, ((n+1)^2\4)-((n-k)\2), ((n-1)^2\4)+((n-k)\2) ) - Paul D. Hanna (pauldhanna(AT)juno.com)
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CROSSREFS
| Cf. A140756, A002620.
Sequence in context: A161621 A095701 A067992 * A100035 A201927 A090244
Adjacent sequences: A140754 A140755 A140756 * A140758 A140759 A140760
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), May 27 2008
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