cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A102856 Sum of 1 or 2 distinct tetrahedral numbers.

Original entry on oeis.org

0, 1, 4, 5, 10, 11, 14, 20, 21, 24, 30, 35, 36, 39, 45, 55, 56, 57, 60, 66, 76, 84, 85, 88, 91, 94, 104, 119, 120, 121, 124, 130, 140, 155, 165, 166, 169, 175, 176, 185, 200, 204, 220, 221, 224, 230, 240, 249, 255, 276, 285, 286, 287, 290, 296, 304, 306
Offset: 1

Views

Author

Jud McCranie, Mar 01 2005

Keywords

Crossrefs

Cf. A102801 (sums if 2 distinct positive)

Programs

  • Maple
    N:= 1000: # for terms <= N
    R:= 0:
    for i from 1 do
      ti:= i*(i+1)*(i+2)/6;
      if ti > N then break fi;
      for j from 0 to i-1 do
         v:= ti + j*(j+1)*(j+2)/6;
         if v > N then break fi;
         R:= R, v;
      od;
    od:
    sort(convert({R},list)); # Robert Israel, Jan 16 2024
  • Mathematica
    Module[{nn=12, tetra}, tetra=Table[(n(n+1)(n+2))/6, {n, nn}]; Union[ Total/@ Subsets[tetra, 2]]] (* James C. McMahon, Jan 12 2024 *)

Extensions

a(1) = 0 prepended by James C. McMahon, Jan 15 2024

A374168 a(n) is the smallest number which can be represented as the sum of two nonzero square pyramidal numbers in exactly n ways, or -1 if no such number exists.

Original entry on oeis.org

2, 60, 9692375
Offset: 1

Views

Author

Ilya Gutkovskiy, Jun 30 2024

Keywords

Comments

There are no further positive terms <= 10^15. - Michael S. Branicky, Jul 01 2024

Examples

			a(2) = 60 = 5 + 55 = 30 + 30.
		

Crossrefs

A374193 a(n) is the smallest number which can be represented as the sum of two nonzero pentagonal pyramidal numbers in exactly n ways, or -1 if no such number exists.

Original entry on oeis.org

2, 1471, 269406
Offset: 1

Views

Author

Ilya Gutkovskiy, Jun 30 2024

Keywords

Comments

There are no further positive terms <= 10^15. - Michael S. Branicky, Jul 01 2024

Examples

			a(2) = 1471 = 1 + 1470 = 288 + 1183.
		

Crossrefs

A374194 a(n) is the smallest number which can be represented as the sum of two nonzero hexagonal pyramidal numbers in exactly n ways, or -1 if no such number exists.

Original entry on oeis.org

2, 5972, 5170425
Offset: 1

Views

Author

Ilya Gutkovskiy, Jun 30 2024

Keywords

Comments

There are no further positive terms <= 10^15. - Michael S. Branicky, Jun 30 2024

Examples

			a(2) = 5972 = 1222 + 4750 = 1925 + 4047.
		

Crossrefs

A374808 a(n) is the smallest number which can be represented as the sum of 3 distinct nonzero tetrahedral numbers in exactly n ways, or -1 if no such number exists.

Original entry on oeis.org

15, 95, 305, 1795, 2366, 12740, 105080, 193060, 231560, 446995, 2422980, 4753420, 5490660, 8205340, 30594200, 137606920, 138532800, 350464520
Offset: 1

Views

Author

Ilya Gutkovskiy, Jul 20 2024

Keywords

Examples

			a(3) = 305 = 1 + 84 + 220 = 20 + 120 + 165 = 56 + 84 + 165.
		

Crossrefs

Extensions

a(12)-a(18) from Michael S. Branicky, Jul 21 2024

A374809 a(n) is the smallest number which can be represented as the sum of 4 distinct nonzero tetrahedral numbers in exactly n ways, or -1 if no such number exists.

Original entry on oeis.org

35, 115, 260, 315, 760, 705, 1310, 1824, 2365, 1915, 2475, 3335, 6240, 4645, 7735, 8455, 12120, 11505, 15440, 13026, 17325, 20020, 24125, 25575, 26400, 32935, 34440, 36575, 40040, 37180, 44265, 50400, 55100, 60060, 56560, 59160, 60620
Offset: 1

Views

Author

Ilya Gutkovskiy, Jul 20 2024

Keywords

Examples

			a(3) = 260 = 1 + 4 + 35 + 220 = 1 + 10 + 84 + 165 = 4 + 35 + 56 + 165.
		

Crossrefs

Showing 1-6 of 6 results.