This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A174066 Irregular triangle, row sums = A000041, left border = A174065. 4
 1, 1, 1, 1, 2, 1, 3, 1, 1, 4, 2, 1, 5, 3, 1, 2, 7, 4, 2, 2, 9, 5, 3, 2, 3, 12, 7, 4, 4, 3, 15, 9, 5, 6, 3, 4, 19, 12, 7, 8, 6, 4, 25, 15, 9, 10, 9, 4, 5, 31, 19, 12, 14, 12, 8, 5, 38, 25, 15, 18, 15, 12, 5, 7, 48, 31, 19, 24, 21, 16, 10, 7, 60, 38, 25, 30, 27, 20, 15, 7, 9, 73, 48, 31, 38, 36 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Left border = A174065: (1, 1, 1, 2, 3, 4, 5, 7, 9, 12,...) * its aerated variant (1, 0, 1, 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 7,...) = A000041, the partition sequence: (1, 1, 2, 3, 5, 7, 11, 15, 22, 30,...). LINKS FORMULA The triangle is the result of three rules after beginning (1, 1, 1, 1,...): Columns >1 are shifted down twice from previous columns; column terms = left border * (left border placed as a heading row); and row sums = A000041, the partition numbers. The rules force the next missing term in the triangle to be the leftmost term in column 1. This is found by taking p(n) for row n, then subtracting the sum of row n terms (minus leftmost term). EXAMPLE Heading and first few rows of the triangle = .1,...1,...1,...2,...3,...4,...5,...7,...9,... = A174065. .1;........................................... = .. 1 (A000041) .1;........................................... = .. 1 .1,...1;...................................... = .. 2 .2,...1;...................................... = .. 3 .3,...1,...1;................................. = .. 5 .4,...2,...1;................................. = .. 7 .5,...3,...1,...2;............................ = ..11 .7,...4,...2,...2;............................ = ..15 .9....5,...3,...2,...3;....................... = ..22 .12,..7,...4,...4,...3;....................... = ..30 .15,..9,...5,...6,...3;...4;.................. = ..42 .19,.12,...7,...8,...6,...4;.................. = ..56 .25,.15,...9,..10,...9,...4,...5;............. = ..77 .31,.19,..12,..14,..12,...8,...5;............. = .101 .38,.25,..15,..18,..15,..12,...5,...7;........ = .135 .48,.31,..19,..24,..21,..16,..10,...7;........ = .176 .60,.38,..25,..30,..27,..20,..15,...7,...9;... = .231 .73,.48,..31,..38,..36,..28,..20,..14,...9;... = .297 ... Example: leftmost term in 8th row has to be 7 = (15 - (4 + 2 + 2)); so we place a 7 as next term in the heading, then multiply * leftmost column. Finally, shift the columns down twice. CROSSREFS Cf. A000041, A174065, A174067. Sequence in context: A135841 A210992 A220484 * A089178 A187489 A116599 Adjacent sequences:  A174063 A174064 A174065 * A174067 A174068 A174069 KEYWORD nonn,tabf AUTHOR Gary W. Adamson, Mar 06 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 22 13:19 EDT 2019. Contains 328318 sequences. (Running on oeis4.)