A076389
Sum of squares of numbers that cannot be written as t*n + u*(n+1) for nonnegative integers t,u.
Original entry on oeis.org
0, 1, 30, 220, 950, 3045, 8036, 18480, 38340, 73425, 131890, 224796, 366730, 576485, 877800, 1300160, 1879656, 2659905, 3693030, 5040700, 6775230, 8980741, 11754380, 15207600, 19467500, 24678225, 31002426, 38622780, 47743570
Offset: 1
- Fred. Schuh, Vragen betreffende een onbepaalde vergelijking, Nieuw Tijdschrift voor Wiskunde, 52 (1964-1965) 193-198.
A076460
Sum of squares of numbers that can be written as t*n + u*(n+1) for nonnegative integers t,u in exactly one way.
Original entry on oeis.org
1, 103, 1130, 6070, 22355, 64981, 160468, 351660, 703365, 1308835, 2297086, 3841058, 6166615, 9562385, 14390440, 21097816, 30228873, 42438495, 58506130, 79350670, 106046171, 139838413, 182162300, 234660100, 299200525, 377898651, 473136678, 587585530, 724227295
Offset: 1
- Fred. Schuh, Vragen betreffende een onbepaalde vergelijking, Nieuw Tijdschrift voor Wiskunde, 52 (1964-1965) 193-198.
-
[n*(n+1)*(7*n^4+2*n^3-6*n^2-n+1)/6: n in [1..50]]; // Vincenzo Librandi, Dec 30 2013
-
seq(1/6*n*(n+1)*(7*n^4+2*n^3-6*n^2-n+1),n=1..30);
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CoefficientList[Series[(1 + 96 x + 430 x^2 + 288 x^3 + 25 x^4)/(1 - x)^7, {x, 0, 50}], x] (* Vincenzo Librandi, Dec 30 2013 *)
LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,103,1130,6070,22355,64981,160468},30] (* Harvey P. Dale, Jul 04 2025 *)
A076461
Sum of squares of numbers that can be written as t*n + u*(n+1) for nonnegative integers t,u in exactly two ways.
Original entry on oeis.org
13, 571, 5306, 26470, 93455, 264313, 640276, 1383276, 2736465, 5047735, 8796238, 14621906, 23357971, 36066485, 54076840, 79027288, 112909461, 158115891, 217490530, 294382270, 392701463, 516979441, 672431036, 865020100, 1101528025, 1389625263, 1737945846, 2156164906
Offset: 1
- Fred. Schuh, Vragen betreffende een onbepaalde vergelijking, Nieuw Tijdschrift voor Wiskunde, 52 (1964-1965) 193-198.
-
[n*(n+1)*(25*n^4+26*n^3-6*n^2-7*n+1)/6: n in [1..50]]; // Vincenzo Librandi, Dec 30 2013
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seq(1/6*n*(n+1)*(25*n^4+26*n^3-6*n^2-7*n+1),n=1..30);
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CoefficientList[Series[(13 + 480 x + 1582 x^2 + 864 x^3 + 61 x^4)/(1 - x)^7, {x, 0, 50}], x] (* Vincenzo Librandi, Dec 30 2013 *)
A076464
Sum of squares of numbers that can be written as t*n + u*(n+1) for nonnegative integers t,u in exactly five ways.
Original entry on oeis.org
145, 4567, 38570, 183670, 630755, 1751365, 4187092, 8957100, 17583765, 32236435, 55893310, 92521442, 147274855, 226710785, 339024040, 494299480, 704782617, 985168335, 1352907730, 1828533070, 2436000875, 3203053117, 4161596540, 5348100100, 6804010525
Offset: 1
- Fred. Schuh, Vragen betreffende een onbepaalde vergelijking, Nieuw Tijdschrift voor Wiskunde, 52 (1964-1965) 193-198.
-
[n*(n+1)*(151*n^4+242*n^3+66*n^2-25*n+1)/6: n in [1..50]]; // Vincenzo Librandi, Dec 30 2013
-
seq(1/6*n*(n+1)*(151*n^4+242*n^3+66*n^2-25*n+1),n=1..30);
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CoefficientList[Series[(145 + 3552 x + 9646 x^2 + 4512 x^3 + 265 x^4)/(1 - x)^7, {x, 0, 50}], x] (* Vincenzo Librandi, Dec 30 2013 *)
A076462
Sum of squares of numbers that can be written as t*n + u*(n+1) for nonnegative integers t,u in exactly three ways.
Original entry on oeis.org
41, 1471, 12938, 62870, 218555, 611821, 1471316, 3161388, 6227565, 11448635, 19895326, 32995586, 52606463, 81092585, 121411240, 177204056, 252895281, 353796663, 486218930, 657589870, 876579011, 1153228901, 1499092988, 1927380100, 2453105525, 3093248691
Offset: 1
- Fred. Schuh, Vragen betreffende een onbepaalde vergelijking, Nieuw Tijdschrift voor Wiskunde, 52 (1964-1965) 193-198.
-
[n*(n+1)*(55*n^4+74*n^3+6*n^2-13*n+1)/6: n in [1..50]]; // Vincenzo Librandi, Dec 30 2013
-
seq(1/6*n*(n+1)*(55*n^4+74*n^3+6*n^2-13*n+1),n=1..30);
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CoefficientList[Series[(41 + 1184 x + 3502 x^2 + 1760 x^3 + 113 x^4)/(1 - x)^7, {x, 0, 50}], x] (* Vincenzo Librandi, Dec 30 2013 *)
A076463
Sum of squares of numbers that can be written as t*n + u*(n+1) for nonnegative integers t,u in exactly four ways.
Original entry on oeis.org
85, 2803, 24026, 115270, 397655, 1107505, 2653588, 5685996, 11176665, 20511535, 35594350, 58962098, 93912091, 144640685, 216393640, 315628120, 450186333, 629480811, 864691330, 1168973470, 1557678815, 2048586793, 2662148156, 3421740100, 4353933025
Offset: 1
- Fred. Schuh, Vragen betreffende een onbepaalde vergelijking, Nieuw Tijdschrift voor Wiskunde, 52 (1964-1965) 193-198.
-
[n*(n+1)*(97*n^4+146*n^3+30*n^2-19*n+1)/6: n in [1..50]]; // Vincenzo Librandi, Dec 30 2013
-
seq(1/6*n*(n+1)*(97*n^4+146*n^3+30*n^2-19*n+1),n=1..30);
-
CoefficientList[Series[(85 + 2208 x + 6190 x^2 + 2976 x^3 + 181 x^4)/(1 - x)^7, {x, 0, 50}], x] (* Vincenzo Librandi, Dec 30 2013 *)
Showing 1-6 of 6 results.