Revision History for A053251
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#70 by Michael De Vlieger at Mon Aug 08 09:39:41 EDT 2022
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#69 by Michel Marcus at Mon Aug 08 09:25:10 EDT 2022
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#68 by Jon E. Schoenfield at Wed Aug 03 21:51:37 EDT 2022
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Discussion
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| Mon Aug 08
| 09:25
| Michel Marcus: yes I was wrong
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#67 by Jon E. Schoenfield at Wed Aug 03 21:50:19 EDT 2022
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| COMMENTS
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Number of ways to express n as distincta partial sumssum of 1 + [1,3] + [1,5] + [1,7] + [1,9] + ... that equal n. ] + .... E.g., a(6)=2 because we have 6 = 1+1+1+1+1+1 = 1+1+3+1+1. - Jon Perry, Jan 01 2004
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Discussion
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| Wed Aug 03
| 21:51
| Jon E. Schoenfield: This seems clearer to me. The “1+1+3+1” (rather than “1+3+1+1”) was a mistake, wasn’t it?
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#66 by Jon E. Schoenfield at Wed Aug 03 21:48:01 EDT 2022
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Number of differentdistinct partial sums of 1+[ + [1,3]+[] + [1,5]+[] + [1,7]+[] + [1,9]+... ] + ... that equal n. E.g., a(6)=2 because we have 6= = 1+1+1+1+1+1= = 1+1+3+1. - Jon Perry, Jan 01 2004
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| STATUS
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proposed
editing
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#65 by Jon E. Schoenfield at Wed Aug 03 03:31:46 EDT 2022
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Discussion
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| Wed Aug 03
| 04:00
| Michel Marcus: Number of different : Number of distinct ??
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#64 by Jon E. Schoenfield at Wed Aug 03 03:31:42 EDT 2022
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Also number of partitions of n such that the largest part occurs exactly once and all the other parts occur exactly twice. Example: a(9)=4 because we have [9],[], [7,1,1],[], [5,2,2] and [3,2,2,1,1]. - Emeric Deutsch, Mar 08 2006
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#63 by Jon E. Schoenfield at Wed Aug 03 03:30:43 EDT 2022
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| NAME
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Coefficients of the '3rd -order' mock theta function psi(q)
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| COMMENTS
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Number of different partial sums of 1+[1,3]+[1,5]+[1,7]+[1,9]+... E.g. ., a(6)=2 because we have 6=1+1+1+1+1+1=1+1+3+1. - Jon Perry, Jan 01 2004
Also number of partitions of n such that the largest part occurs exactly once and all the other parts occur exactly twice. Example: a(9)=4 because we have [9],[7,1,1],[5,2,2] and [3,2,2,1,1]. - Emeric Deutsch, Mar 08 2006
For _Emeric Deutsch'_'s comment above, (1) this appears to be an alternately equal case of A122130, (2) the ordered version (compositions) is A239327, (3) allowing any length gives A351006, (4) the even-length version is A351007. - Gus Wiseman, Feb 25 2022
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| REFERENCES
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Srinivasa Ramanujan, Collected Papers, Chelsea, New York, 1962, pp. 354-355.
Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 31.
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| FORMULA
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G.f.: psi(q) = sum(Sum_{n>=1, } q^(n^2) / ( (1-q)*(1-q^3)*...*(1-q^(2*n-1)) ) ).)) ).
G.f.: sum(Sum_{k>=1, } q^k*prod(Product_{j=1..k-1, } (1+q^(2*j) ) ), ()) (see the Fine reference, p. 58, Eq. (26,53)). - Emeric Deutsch, Mar 08 2006
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| CROSSREFS
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Other '3rd -order' mock theta functions are at A000025, A053250, A053252, A053253, A053254, A053255.
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approved
editing
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#62 by N. J. A. Sloane at Fri Mar 11 12:41:19 EST 2022
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#61 by Gus Wiseman at Fri Feb 25 11:32:35 EST 2022
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Discussion
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| Fri Feb 25
| 12:06
| Wesley Ivan Hurt: Alois simply lives life in all caps.
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